Investigation On Quantum Phase Transitions By Using Quantum Renormalization Group And Quantum Correlation

A new discipline quantum information science is found by the integration development of quantum mechanics,information theory and computer science.Quantum informa-tion is not the simple extension of classical information,it is the advanced interdisciplinary subject that is set up by using the interference,nonlocality,and randomness of the quantum state.The research contents of quantum information is widely,including quantum cryptography,quantum communication,quantum computer,quantum simulation and quantum measurement and so on.As a new subject,the development of quantum information grew rapidly.The world's first quantum satellite has been successfully launched.Quantum key distribution theory and experiment are gradually perfected.The universal quantum computer and adiabatic quantum computer also have made great progress.All these indicate the bright future of quantum information technology.Furthermore,the development of quantum information gain breakthrough progress in some basic physics problem,such as quantum phase transitions(QPT).QPT is completely induced by quantum fluctuations at absolute zero temperature.As one of the important subjects in condensed matter physics,QPT indicates that the ground state of a manybody system changes abruptly when varying a physical parameter such as pressure,magnetic field or constituent.The rapid development of quantum information science provides us a good means to understand the nature of QPT.In this dissertation,by combing quantum renormalization group(QRG)and some basic con-cepts in quantum information,such as quantum entanglement,quantum correlation,quantum nonlocality,and quantum coherence and so on.We investigate the QPT in spin system and get some meaningful results.In the first chapter,the background and related progress on quantum information theory,QPT and spin system are reviewed briefly and then,a brief outline of this dissertation is presented.In the second chapter,we study the global entanglement and QPT in the Heisenberg XXZ model by using negativity.We analyze the QPT properties combing the QRG method.We investigate the critical properties of quantum entanglement and discuss the monogamy relation in this block model.The results show that the global negativity can be used to detect the occurrence of QPT and the derivative of global negativity tends to diverge at the critical point.The global negativity against the chain size shows linear behavior.The results demonstrate that the QRG implementation of global negativity can genuinely captures the critical property of the model.The residual entanglement based on monogamy relation catches the critical behavior of the XXZ model too.The critical exponent ? of the entanglement has no change with the variation of entanglement measures because the critical exponent ? directly associates with the correlation length exponent v,i.e.,?=1/v.In the third chapter,we have used the methods of quantum correlation to analyze the critical behavior of Ising model in transverse field(ITF).In 2001,Zurek et al.have concluded that entanglement does not account for all nonclassical correlations and even those separable states also can promote the speed of quantum computation because they contain nonclassical correlations that can be demonstrated by quantum discord.This bright new chance for quantum information science.Inspired by the meaningful results about quantum discord,many similar quantum correlation measures based on information-theoretic have been proposed.The investigations on these methods also have received much attention.Based on ITF,we investigate the general and special properties of different quantum correlation when they apply to study QPT.Our results indicate that the critical behavior can be described by quantum correlation or Bell violation.These quantum-information theoretic measures share the same singularity and scaling behavior in QRG procedure.The critical exponent which relates with the correlation length exponent will remain the value 1 even with the variation of different quantum correlation measures.Based on numerical computation,we have conjectured that the correlation length can be easily gotten by applying the QRG theory.The differences among each quantum correlation measures also are given.In the fourth chapter,we discuss the QPT in two-dimensional XY model through quantum correlation and monogamy relation.Except for the one-dimensional systems,the quantum correlation and QPT in two-dimensional spin systems also are very important because there are many two-dimensional materials in nature.The research on these models will promote the understanding of ground-state properties,correlation length,and critical point in two-dimensional model.As opposed to the one-dimensional case,the two-dimensional system size increases rapidly because we select five-site as one block.Further,the critical point and the saturated values can be reached in the lesser number of QRG iterations.The scaling behavior was investigated through determination of the quantum correlation exponent which demonstrates how the critical point is attained as the size becomes large.Remarkably,we have obtained identical critical exponent for entanglement,quantum correlation and Bell violation.Moreover,we have studied multipartite quantum correlations with the monogamy relation of concurrence and quantum discord.The results show that the two quantities are monogamous in this two-dimensional XY model,and they can be used to detect the QPT.In the fifth chapter,the quantum coherence and its dynamics properties are analyzed.Quantum coherence comes from state superposition principle of quantum mechanics,it is the core notion in quantum mechanics and quantum information and it also is the basis of quantum entanglement and quantum correlation.We firstly discuss the QPT in one-dimensional XY system by means of quantum coherence.We select three spin as one block to implement QRG.Through studying the quantum coherence of the whole block state and the reduced density matrix,we find they obey conservation law.And they all can detect the QPT point and show scaling behavior.Furthermore,we investigate the dynamics behavior of ITF by using quantum coherence.We give the dependence of the quantum coherence on the system size increase and analyze the dynamics behavior with time.We also adopt the quantum discord and classical correlation to study the evolution in this model as contrasted with quantum coherence.In the sixth chapter,we present the summary of this dissertation and some prospects for the future study.